/*
* math.h
*
* ANSI/POSIX + Microsoft compatible mathematical function prototypes,
* associated macros, and manifest constant definitions.
*
* $Id: math.h,v 1e905d042bda 2017/11/28 17:33:30 keith $
*
* Written by Colin Peters <colin@bird.fu.is.saga-u.ac.jp>
* Copyright (C) 1997-2009, 2014-2016, MinGW.org Project.
*
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice, this permission notice, and the following
* disclaimer shall be included in all copies or substantial portions of
* the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OF OR OTHER
* DEALINGS IN THE SOFTWARE.
*
*/
#ifndef _MATH_H
#define _MATH_H
#pragma GCC system_header
/* All the headers include this file.
*/
#include <_mingw.h>
/* Types for the _exception structure.
*/
#define _DOMAIN 1 /* domain error in argument */
#define _SING 2 /* singularity */
#define _OVERFLOW 3 /* range overflow */
#define _UNDERFLOW 4 /* range underflow */
#define _TLOSS 5 /* total loss of precision */
#define _PLOSS 6 /* partial loss of precision */
#if ! defined __STRICT_ANSI__ && ! defined _NO_OLDNAMES
/*
* Exception types with non-ANSI names for compatibility.
*/
#define DOMAIN _DOMAIN
#define SING _SING
#define OVERFLOW _OVERFLOW
#define UNDERFLOW _UNDERFLOW
#define TLOSS _TLOSS
#define PLOSS _PLOSS
#endif /* !__STRICT_ANSI__ && !_NO_OLDNAMES */
#if _POSIX_C_SOURCE || defined _USE_MATH_DEFINES
/* Traditional/XOPEN math constants (double precison). MSVC makes these
* available, only if _USE_MATH_DEFINES is specified; POSIX does so also,
* when _POSIX_C_SOURCE is defined and non-zero, (as will be the case by
* default in MinGW, unless __STRICT_ANSI__ checking is in effect).
*/
#define M_E 2.7182818284590452354
#define M_LOG2E 1.4426950408889634074
#define M_LOG10E 0.43429448190325182765
#define M_LN2 0.69314718055994530942
#define M_LN10 2.30258509299404568402
#define M_PI 3.14159265358979323846
#define M_PI_2 1.57079632679489661923
#define M_PI_4 0.78539816339744830962
#define M_1_PI 0.31830988618379067154
#define M_2_PI 0.63661977236758134308
#define M_2_SQRTPI 1.12837916709551257390
#define M_SQRT2 1.41421356237309504880
#define M_SQRT1_2 0.70710678118654752440
#endif
/* These are also defined in MinGW float.h; needed here as well,
* to work around GCC build issues.
*
* FIXME: Since they're needed both in MinGW float.h and here,
* they should be moved to a common "parts" header.
*/
#if ! defined __STRICT_ANSI__ && ! defined __MINGW_FPCLASS_DEFINED
#define __MINGW_FPCLASS_DEFINED 1
/* IEEE 754 classication
*/
#define _FPCLASS_SNAN 0x0001 /* Signaling "Not a Number" */
#define _FPCLASS_QNAN 0x0002 /* Quiet "Not a Number" */
#define _FPCLASS_NINF 0x0004 /* Negative Infinity */
#define _FPCLASS_NN 0x0008 /* Negative Normal */
#define _FPCLASS_ND 0x0010 /* Negative Denormal */
#define _FPCLASS_NZ 0x0020 /* Negative Zero */
#define _FPCLASS_PZ 0x0040 /* Positive Zero */
#define _FPCLASS_PD 0x0080 /* Positive Denormal */
#define _FPCLASS_PN 0x0100 /* Positive Normal */
#define _FPCLASS_PINF 0x0200 /* Positive Infinity */
#endif /* !__STRICT_ANSI__ && !__MINGW_FPCLASS_DEFINED */
#ifndef RC_INVOKED
_BEGIN_C_DECLS
/* HUGE_VAL is returned by strtod when the value would overflow the
* representation of 'double'. There are other uses as well.
*
* __imp__HUGE is a pointer to the actual variable _HUGE in
* MSVCRT.DLL. If we used _HUGE directly we would get a pointer
* to a thunk function.
*
* NOTE: The CRTDLL version uses _HUGE_dll instead.
*/
#if __MINGW_GNUC_PREREQ(3, 3)
#define HUGE_VAL __builtin_huge_val()
#else
#ifndef __DECLSPEC_SUPPORTED
#ifdef __MSVCRT__
extern double *_imp___HUGE;
#define HUGE_VAL (*_imp___HUGE)
#else /* CRTDLL */
extern double *_imp___HUGE_dll;
#define HUGE_VAL (*_imp___HUGE_dll)
#endif
#else /* __DECLSPEC_SUPPORTED */
#ifdef __MSVCRT__
__MINGW_IMPORT double _HUGE;
#define HUGE_VAL _HUGE
#else /* CRTDLL */
__MINGW_IMPORT double _HUGE_dll;
#define HUGE_VAL _HUGE_dll
#endif
#endif /* __DECLSPEC_SUPPORTED */
#endif /* __MINGW_GNUC_PREREQ(3, 3) */
struct _exception
{
int type;
char *name;
double arg1;
double arg2;
double retval;
};
_CRTIMP double __cdecl sin (double);
_CRTIMP double __cdecl cos (double);
_CRTIMP double __cdecl tan (double);
_CRTIMP double __cdecl sinh (double);
_CRTIMP double __cdecl cosh (double);
_CRTIMP double __cdecl tanh (double);
_CRTIMP double __cdecl asin (double);
_CRTIMP double __cdecl acos (double);
_CRTIMP double __cdecl atan (double);
_CRTIMP double __cdecl atan2 (double, double);
_CRTIMP double __cdecl exp (double);
_CRTIMP double __cdecl log (double);
_CRTIMP double __cdecl log10 (double);
_CRTIMP double __cdecl pow (double, double);
_CRTIMP double __cdecl sqrt (double);
_CRTIMP double __cdecl ceil (double);
_CRTIMP double __cdecl floor (double);
_CRTIMP double __cdecl fabs (double);
_CRTIMP double __cdecl ldexp (double, int);
_CRTIMP double __cdecl frexp (double, int*);
_CRTIMP double __cdecl modf (double, double*);
_CRTIMP double __cdecl fmod (double, double);
#if 0
/* Excess precision when using a 64-bit mantissa for FPU math ops can
* cause unexpected results with some of the MSVCRT math functions. For
* example, unless the function return value is stored (truncating to
* 53-bit mantissa), calls to pow with both x and y as integral values
* sometimes produce a non-integral result.
*
* One workaround is to reset the FPU env to 53-bit mantissa
* by a call to fesetenv (FE_PC53_ENV). Amother is to force storage
* of the return value of individual math functions using wrappers.
* NB, using these wrappers will disable builtin math functions and
* hence disable the folding of function results at compile time when
* arguments are constant.
*/
#define __DEFINE_FLOAT_STORE_MATHFN_D1(fn1) \
static __inline__ double \
__float_store_ ## fn1 (double x) \
{ \
__volatile__ double res = (fn1) (x); \
return res; \
}
#define __DEFINE_FLOAT_STORE_MATHFN_D2(fn2) \
static __inline__ double \
__float_store_ ## fn2 (double x, double y) \
{ \
__volatile__ double res = (fn2) (x, y); \
return res; \
}
/* For example, here is how to force the result of the pow function
* to be stored:
*/
#undef pow
/* Define the ___float_store_pow function and use it instead of pow().
*/
__DEFINE_FLOAT_STORE_MATHFN_D2 (pow)
#define pow __float_store_pow
#endif
#ifndef __STRICT_ANSI__
struct _complex
{ /* Complex number (for _cabs). This is the MS version; the
* ISO-C99 counterpart, _Complex, is an intrinsic type in GCC,
* and 'complex' is defined as a macro. See <complex.h>
*/
double x; /* Real part */
double y; /* Imaginary part */
};
_CRTIMP double __cdecl _cabs (struct _complex);
_CRTIMP double __cdecl _hypot (double, double);
_CRTIMP double __cdecl _j0 (double);
_CRTIMP double __cdecl _j1 (double);
_CRTIMP double __cdecl _jn (int, double);
_CRTIMP double __cdecl _y0 (double);
_CRTIMP double __cdecl _y1 (double);
_CRTIMP double __cdecl _yn (int, double);
_CRTIMP int __cdecl _matherr (struct _exception *);
/* These are also declared in MinGW's <float.h>; we need them
* here as well to work around GCC build issues.
*/
/* BEGIN FLOAT.H COPY */
/*
* IEEE recommended functions
*/
_CRTIMP double __cdecl _chgsign (double);
_CRTIMP double __cdecl _copysign (double, double);
_CRTIMP double __cdecl _logb (double);
_CRTIMP double __cdecl _nextafter (double, double);
_CRTIMP double __cdecl _scalb (double, long);
_CRTIMP int __cdecl _finite (double);
_CRTIMP int __cdecl _fpclass (double);
_CRTIMP int __cdecl _isnan (double);
/* END FLOAT.H COPY */
#ifndef _NO_OLDNAMES
/* Non-underscored versions of non-ANSI functions.
* These reside in liboldnames.a.
*/
_CRTIMP double __cdecl j0 (double);
_CRTIMP double __cdecl j1 (double);
_CRTIMP double __cdecl jn (int, double);
_CRTIMP double __cdecl y0 (double);
_CRTIMP double __cdecl y1 (double);
_CRTIMP double __cdecl yn (int, double);
_CRTIMP double __cdecl chgsign (double);
/*
* scalb() is a GCC built-in.
* Exclude this _scalb() stub; the semantics are incompatible
* with the built-in implementation.
*
_CRTIMP double __cdecl scalb (double, long);
*
*/
_CRTIMP int __cdecl finite (double);
_CRTIMP int __cdecl fpclass (double);
#define FP_SNAN _FPCLASS_SNAN
#define FP_QNAN _FPCLASS_QNAN
#define FP_NINF _FPCLASS_NINF
#define FP_PINF _FPCLASS_PINF
#define FP_NDENORM _FPCLASS_ND
#define FP_PDENORM _FPCLASS_PD
#define FP_NZERO _FPCLASS_NZ
#define FP_PZERO _FPCLASS_PZ
#define FP_NNORM _FPCLASS_NN
#define FP_PNORM _FPCLASS_PN
#endif /* !_NO_OLDNAMES */
#if _WIN32_WINNT >= _WIN32_WINNT_WINXP || __MSVCRT_VERSION__ >= __MSVCR70_DLL
/*
* This requires WinXP, or MSVCR70.DLL, or later.
*/
_CRTIMP int __cdecl _set_SSE2_enable (int);
#endif /* >= WINXP || >= __MSVCR70_DLL */
#endif /* !__STRICT_ANSI__ */
#if defined __cplusplus || defined _ISOC99_SOURCE
# if __MINGW_GNUC_PREREQ(3, 3)
# define HUGE_VALF __builtin_huge_valf()
# define HUGE_VALL __builtin_huge_vall()
# define INFINITY __builtin_inf()
# define NAN __builtin_nan("")
# else
extern const float __INFF;
extern const long double __INFL;
extern const double __QNAN;
# define HUGE_VALF __INFF
# define HUGE_VALL __INFL
# define INFINITY HUGE_VALF
# define NAN __QNAN
# endif /* __MINGW_GNUC_PREREQ(3, 3) */
/* Use the compiler's internal definition for FLT_EVAL_METHOD, if one
* is available, to establish appropriate float_t and double_t typedefs;
* in the case of GCC, this is specified as __FLT_EVAL_METHOD__, which
* is expected to be assigned standardized values of 0, 1, or 2, (or
* exceptionally, a value of -1, representing indeterminacy).
*/
#if ! defined __FLT_EVAL_METHOD__ || __valueless(__FLT_EVAL_METHOD__) \
|| (__FLT_EVAL_METHOD__ - 0) < 0 || (__FLT_EVAL_METHOD__ - 0) > 1
/* __FLT_EVAL_METHOD__ has not been defined, or it is defined with no
* value, or with a value of -1 (or less), or a value of 2 or more; in
* the specific case of a value of 2, this represents an explicit choice
* of the IX387 FPU configuration, while in each of the other cases, we
* implicitly fall back to this same default configuration.
*
* NOTE: this configuration is correct for X87 FPU computations, (for
* which __FLT_EVAL_METHOD__ is correctly specified as 2); however...
*/
# if defined __FLT_EVAL_METHOD__ && (__FLT_EVAL_METHOD__ - 0) != 2
/* ...due to a GCC bug, introduced in GCC-6 and persisting into later
* versions, it may be selected via __FLT_EVAL_METHOD__ == -1, for the
* case of the "-msse -mfpmath=sse" option combination. In this case,
* it is (at best) an unsatisfactory compromise; to avoid it, you may
* prefer to adopt "-mfpmath=387", or "-msse2 -mfpmath=sse" instead.
*/
# warning "Default FLT_EVAL_METHOD is inderminate; assuming X87 semantics."
# endif
typedef long double float_t;
typedef long double double_t;
#else
/* __FLT_EVAL_METHOD__ must have been defined with an explicit value
* of either 0 or 1; select the corresponding SSE configuration which
* is applicable in each case.
*/
# if __FLT_EVAL_METHOD__ == 0
typedef float float_t;
typedef double double_t;
# else /* __FLT_EVAL_METHOD__ == 1 */
typedef double float_t;
typedef double double_t;
# endif
#endif
/* 7.12.3.1
* Return values for fpclassify.
* These are based on Intel x87 fpu condition codes
* in the high byte of status word and differ from
* the return values for MS IEEE 754 extension _fpclass()
*/
#define FP_NAN 0x0100
#define FP_NORMAL 0x0400
#define FP_INFINITE (FP_NAN | FP_NORMAL)
#define FP_ZERO 0x4000
#define FP_SUBNORMAL (FP_NORMAL | FP_ZERO)
/* 0x0200 is signbit mask */
/* We can't inline float or double, because we want to ensure
* truncation to semantic type before classification; (a normal
* long double value might become subnormal when converted to
* double, and zero when converted to float.)
*/
extern int __cdecl __fpclassifyf (float);
extern int __cdecl __fpclassify (double);
extern int __cdecl __fpclassifyl (long double);
#ifndef __NO_INLINE__
__CRT_INLINE int __cdecl __fpclassifyl (long double x){
unsigned short sw;
__asm__ ("fxam; fstsw %%ax;" : "=a" (sw): "t" (x));
return sw & (FP_NAN | FP_NORMAL | FP_ZERO );
}
#endif
#define fpclassify(x) (sizeof (x) == sizeof (float) ? __fpclassifyf (x) \
: sizeof (x) == sizeof (double) ? __fpclassify (x) \
: __fpclassifyl (x))
/* 7.12.3.2 */
#define isfinite(x) ((fpclassify(x) & FP_NAN) == 0)
/* 7.12.3.3 */
#define isinf(x) (fpclassify(x) == FP_INFINITE)
/* 7.12.3.4 */
/* We don't need to worry about truncation here:
* a NaN stays a NaN.
*/
extern int __cdecl __isnan (double);
extern int __cdecl __isnanf (float);
extern int __cdecl __isnanl (long double);
#ifndef __NO_INLINE__
__CRT_INLINE int __cdecl __isnan (double _x)
{
unsigned short sw;
__asm__ ("fxam;"
"fstsw %%ax": "=a" (sw) : "t" (_x));
return (sw & (FP_NAN | FP_NORMAL | FP_INFINITE | FP_ZERO | FP_SUBNORMAL))
== FP_NAN;
}
__CRT_INLINE int __cdecl __isnanf (float _x)
{
unsigned short sw;
__asm__ ("fxam;"
"fstsw %%ax": "=a" (sw) : "t" (_x));
return (sw & (FP_NAN | FP_NORMAL | FP_INFINITE | FP_ZERO | FP_SUBNORMAL))
== FP_NAN;
}
__CRT_INLINE int __cdecl __isnanl (long double _x)
{
unsigned short sw;
__asm__ ("fxam;"
"fstsw %%ax": "=a" (sw) : "t" (_x));
return (sw & (FP_NAN | FP_NORMAL | FP_INFINITE | FP_ZERO | FP_SUBNORMAL))
== FP_NAN;
}
#endif
#define isnan(x) (sizeof (x) == sizeof (float) ? __isnanf (x) \
: sizeof (x) == sizeof (double) ? __isnan (x) \
: __isnanl (x))
/* 7.12.3.5 */
#define isnormal(x) (fpclassify(x) == FP_NORMAL)
/* 7.12.3.6 The signbit macro */
extern int __cdecl __signbit (double);
extern int __cdecl __signbitf (float);
extern int __cdecl __signbitl (long double);
#ifndef __NO_INLINE__
__CRT_INLINE int __cdecl __signbit (double x) {
unsigned short stw;
__asm__ ( "fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
return (stw & 0x0200) != 0;
}
__CRT_INLINE int __cdecl __signbitf (float x) {
unsigned short stw;
__asm__ ("fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
return (stw & 0x0200) != 0;
}
__CRT_INLINE int __cdecl __signbitl (long double x) {
unsigned short stw;
__asm__ ("fxam; fstsw %%ax;": "=a" (stw) : "t" (x));
return (stw & 0x0200) != 0;
}
#endif
#define signbit(x) (sizeof (x) == sizeof (float) ? __signbitf (x) \
: sizeof (x) == sizeof (double) ? __signbit (x) \
: __signbitl (x))
/* 7.12.4 Trigonometric functions: double in C89
*/
extern float __cdecl sinf (float);
extern long double __cdecl sinl (long double);
extern float __cdecl cosf (float);
extern long double __cdecl cosl (long double);
extern float __cdecl tanf (float);
extern long double __cdecl tanl (long double);
extern float __cdecl asinf (float);
extern long double __cdecl asinl (long double);
extern float __cdecl acosf (float);
extern long double __cdecl acosl (long double);
extern float __cdecl atanf (float);
extern long double __cdecl atanl (long double);
extern float __cdecl atan2f (float, float);
extern long double __cdecl atan2l (long double, long double);
/* 7.12.5 Hyperbolic functions: double in C89
*/
extern float __cdecl sinhf (float);
#ifndef __NO_INLINE__
__CRT_INLINE float __cdecl sinhf (float x)
{return (float) sinh (x);}
#endif
extern long double __cdecl sinhl (long double);
extern float __cdecl coshf (float);
#ifndef __NO_INLINE__
__CRT_INLINE float __cdecl coshf (float x)
{return (float) cosh (x);}
#endif
extern long double __cdecl coshl (long double);
extern float __cdecl tanhf (float);
#ifndef __NO_INLINE__
__CRT_INLINE float __cdecl tanhf (float x)
{return (float) tanh (x);}
#endif
extern long double __cdecl tanhl (long double);
/* Inverse hyperbolic trig functions */
/* 7.12.5.1 */
extern double __cdecl acosh (double);
extern float __cdecl acoshf (float);
extern long double __cdecl acoshl (long double);
/* 7.12.5.2 */
extern double __cdecl asinh (double);
extern float __cdecl asinhf (float);
extern long double __cdecl asinhl (long double);
/* 7.12.5.3 */
extern double __cdecl atanh (double);
extern float __cdecl atanhf (float);
extern long double __cdecl atanhl (long double);
/* Exponentials and logarithms */
/* 7.12.6.1 Double in C89 */
extern float __cdecl expf (float);
#ifndef __NO_INLINE__
__CRT_INLINE float __cdecl expf (float x)
{return (float) exp (x);}
#endif
extern long double __cdecl expl (long double);
/* 7.12.6.2 */
extern double __cdecl exp2(double);
extern float __cdecl exp2f(float);
extern long double __cdecl exp2l(long double);
/* 7.12.6.3 The expm1 functions */
/* TODO: These could be inlined */
extern double __cdecl expm1(double);
extern float __cdecl expm1f(float);
extern long double __cdecl expm1l(long double);
/* 7.12.6.4 Double in C89 */
extern float __cdecl frexpf (float, int*);
#ifndef __NO_INLINE__
__CRT_INLINE float __cdecl frexpf (float x, int* expn)
{return (float) frexp (x, expn);}
#endif
extern long double __cdecl frexpl (long double, int*);
/* 7.12.6.5 */
#define FP_ILOGB0 ((int)0x80000000)
#define FP_ILOGBNAN ((int)0x80000000)
extern int __cdecl ilogb (double);
extern int __cdecl ilogbf (float);
extern int __cdecl ilogbl (long double);
/* 7.12.6.6 Double in C89 */
extern float __cdecl ldexpf (float, int);
#ifndef __NO_INLINE__
__CRT_INLINE float __cdecl ldexpf (float x, int expn)
{return (float) ldexp (x, expn);}
#endif
extern long double __cdecl ldexpl (long double, int);
/* 7.12.6.7 Double in C89 */
extern float __cdecl logf (float);
extern long double __cdecl logl (long double);
/* 7.12.6.8 Double in C89 */
extern float __cdecl log10f (float);
extern long double __cdecl log10l (long double);
/* 7.12.6.9 */
extern double __cdecl log1p(double);
extern float __cdecl log1pf(float);
extern long double __cdecl log1pl(long double);
/* 7.12.6.10 */
extern double __cdecl log2 (double);
extern float __cdecl log2f (float);
extern long double __cdecl log2l (long double);
/* 7.12.6.11 */
extern double __cdecl logb (double);
extern float __cdecl logbf (float);
extern long double __cdecl logbl (long double);
/* Inline versions. GCC-4.0+ can do a better fast-math optimization
* with __builtins.
*/
#ifndef __NO_INLINE__
#if !(__MINGW_GNUC_PREREQ (4, 0) && defined __FAST_MATH__ )
__CRT_INLINE double __cdecl logb (double x)
{
double res;
__asm__ ("fxtract\n\t"
"fstp %%st" : "=t" (res) : "0" (x));
return res;
}
__CRT_INLINE float __cdecl logbf (float x)
{
float res;
__asm__ ("fxtract\n\t"
"fstp %%st" : "=t" (res) : "0" (x));
return res;
}
__CRT_INLINE long double __cdecl logbl (long double x)
{
long double res;
__asm__ ("fxtract\n\t"
"fstp %%st" : "=t" (res) : "0" (x));
return res;
}
#endif /* !__FAST_MATH__ || !__MINGW_GNUC_PREREQ (4, 0) */
#endif /* !__NO_INLINE__ */
/* 7.12.6.12 Double in C89 */
extern float __cdecl modff (float, float*);
extern long double __cdecl modfl (long double, long double*);
/* 7.12.6.13 */
extern double __cdecl scalbn (double, int);
extern float __cdecl scalbnf (float, int);
extern long double __cdecl scalbnl (long double, int);
extern double __cdecl scalbln (double, long);
extern float __cdecl scalblnf (float, long);
extern long double __cdecl scalblnl (long double, long);
/* 7.12.7.1 */
/* Implementations adapted from Cephes versions */
extern double __cdecl cbrt (double);
extern float __cdecl cbrtf (float);
extern long double __cdecl cbrtl (long double);
/* 7.12.7.2 The fabs functions: Double in C89 */
extern float __cdecl fabsf (float x);
extern long double __cdecl fabsl (long double x);
/* 7.12.7.3 */
extern double __cdecl hypot (double, double); /* in libmoldname.a */
extern float __cdecl hypotf (float, float);
extern long double __cdecl hypotl (long double, long double);
/* 7.12.7.4 The pow functions. Double in C89 */
extern float __cdecl powf (float, float);
extern long double __cdecl powl (long double, long double);
/* 7.12.7.5 The sqrt functions. Double in C89. */
extern float __cdecl sqrtf (float);
extern long double __cdecl sqrtl (long double);
/* 7.12.8.1 The erf functions */
extern double __cdecl erf (double);
extern float __cdecl erff (float);
extern long double __cdecl erfl (long double);
/* 7.12.8.2 The erfc functions */
extern double __cdecl erfc (double);
extern float __cdecl erfcf (float);
extern long double __cdecl erfcl (long double);
/* 7.12.8.3 The lgamma functions */
extern double __cdecl lgamma (double);
extern float __cdecl lgammaf (float);
extern long double __cdecl lgammal (long double);
/* 7.12.8.4 The tgamma functions */
extern double __cdecl tgamma (double);
extern float __cdecl tgammaf (float);
extern long double __cdecl tgammal (long double);
/* 7.12.9.1 Double in C89 */
extern float __cdecl ceilf (float);
extern long double __cdecl ceill (long double);
/* 7.12.9.2 Double in C89 */
extern float __cdecl floorf (float);
extern long double __cdecl floorl (long double);
/* 7.12.9.3 */
extern double __cdecl nearbyint ( double);
extern float __cdecl nearbyintf (float);
extern long double __cdecl nearbyintl (long double);
/* 7.12.9.4 */
/* round, using fpu control word settings */
extern double __cdecl rint (double);
extern float __cdecl rintf (float);
extern long double __cdecl rintl (long double);
/* 7.12.9.5 */
extern long __cdecl lrint (double);
extern long __cdecl lrintf (float);
extern long __cdecl lrintl (long double);
extern long long __cdecl llrint (double);
extern long long __cdecl llrintf (float);
extern long long __cdecl llrintl (long double);
/* Inline versions of above.
* GCC 4.0+ can do a better fast-math job with __builtins.
*/
#ifndef __NO_INLINE__
#if !(__MINGW_GNUC_PREREQ (4, 0) && defined __FAST_MATH__ )
__CRT_INLINE double __cdecl rint (double x)
{
double retval;
__asm__ ("frndint;": "=t" (retval) : "0" (x));
return retval;
}
__CRT_INLINE float __cdecl rintf (float x)
{
float retval;
__asm__ ("frndint;" : "=t" (retval) : "0" (x) );
return retval;
}
__CRT_INLINE long double __cdecl rintl (long double x)
{
long double retval;
__asm__ ("frndint;" : "=t" (retval) : "0" (x) );
return retval;
}
__CRT_INLINE long __cdecl lrint (double x)
{
long retval;
__asm__ __volatile__
("fistpl %0" : "=m" (retval) : "t" (x) : "st");
return retval;
}
__CRT_INLINE long __cdecl lrintf (float x)
{
long retval;
__asm__ __volatile__
("fistpl %0" : "=m" (retval) : "t" (x) : "st");
return retval;
}
__CRT_INLINE long __cdecl lrintl (long double x)
{
long retval;
__asm__ __volatile__
("fistpl %0" : "=m" (retval) : "t" (x) : "st");
return retval;
}
__CRT_INLINE long long __cdecl llrint (double x)
{
long long retval;
__asm__ __volatile__
("fistpll %0" : "=m" (retval) : "t" (x) : "st");
return retval;
}
__CRT_INLINE long long __cdecl llrintf (float x)
{
long long retval;
__asm__ __volatile__
("fistpll %0" : "=m" (retval) : "t" (x) : "st");
return retval;
}
__CRT_INLINE long long __cdecl llrintl (long double x)
{
long long retval;
__asm__ __volatile__
("fistpll %0" : "=m" (retval) : "t" (x) : "st");
return retval;
}
#endif /* !__FAST_MATH__ || !__MINGW_GNUC_PREREQ (4,0) */
#endif /* !__NO_INLINE__ */
/* 7.12.9.6 */
/* round away from zero, regardless of fpu control word settings */
extern double __cdecl round (double);
extern float __cdecl roundf (float);
extern long double __cdecl roundl (long double);
/* 7.12.9.7 */
extern long __cdecl lround (double);
extern long __cdecl lroundf (float);
extern long __cdecl lroundl (long double);
extern long long __cdecl llround (double);
extern long long __cdecl llroundf (float);
extern long long __cdecl llroundl (long double);
/* 7.12.9.8 */
/* round towards zero, regardless of fpu control word settings */
extern double __cdecl trunc (double);
extern float __cdecl truncf (float);
extern long double __cdecl truncl (long double);
/* 7.12.10.1 Double in C89 */
extern float __cdecl fmodf (float, float);
extern long double __cdecl fmodl (long double, long double);
/* 7.12.10.2 */
extern double __cdecl remainder (double, double);
extern float __cdecl remainderf (float, float);
extern long double __cdecl remainderl (long double, long double);
/* 7.12.10.3 */
extern double __cdecl remquo(double, double, int *);
extern float __cdecl remquof(float, float, int *);
extern long double __cdecl remquol(long double, long double, int *);
/* 7.12.11.1 */
extern double __cdecl copysign (double, double); /* in libmoldname.a */
extern float __cdecl copysignf (float, float);
extern long double __cdecl copysignl (long double, long double);
/* 7.12.11.2 Return a NaN */
extern double __cdecl nan(const char *tagp);
extern float __cdecl nanf(const char *tagp);
extern long double __cdecl nanl(const char *tagp);
#ifndef __STRICT_ANSI__
#define _nan() nan("")
#define _nanf() nanf("")
#define _nanl() nanl("")
#endif
/* 7.12.11.3 */
extern double __cdecl nextafter (double, double); /* in libmoldname.a */
extern float __cdecl nextafterf (float, float);
extern long double __cdecl nextafterl (long double, long double);
/* 7.12.11.4 The nexttoward functions */
extern double __cdecl nexttoward (double, long double);
extern float __cdecl nexttowardf (float, long double);
extern long double __cdecl nexttowardl (long double, long double);
/* 7.12.12.1 */
/* x > y ? (x - y) : 0.0 */
extern double __cdecl fdim (double x, double y);
extern float __cdecl fdimf (float x, float y);
extern long double __cdecl fdiml (long double x, long double y);
/* fmax and fmin.
NaN arguments are treated as missing data: if one argument is a NaN
and the other numeric, then these functions choose the numeric
value. */
/* 7.12.12.2 */
extern double __cdecl fmax (double, double);
extern float __cdecl fmaxf (float, float);
extern long double __cdecl fmaxl (long double, long double);
/* 7.12.12.3 */
extern double __cdecl fmin (double, double);
extern float __cdecl fminf (float, float);
extern long double __cdecl fminl (long double, long double);
/* 7.12.13.1 */
/* return x * y + z as a ternary op */
extern double __cdecl fma (double, double, double);
extern float __cdecl fmaf (float, float, float);
extern long double __cdecl fmal (long double, long double, long double);
/* 7.12.14
* With these functions, comparisons involving quiet NaNs set the FP
* condition code to "unordered". The IEEE floating-point spec
* dictates that the result of floating-point comparisons should be
* false whenever a NaN is involved, with the exception of the != op,
* which always returns true: yes, (NaN != NaN) is true).
*/
#if __GNUC__ >= 3
#define isgreater(x, y) __builtin_isgreater(x, y)
#define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
#define isless(x, y) __builtin_isless(x, y)
#define islessequal(x, y) __builtin_islessequal(x, y)
#define islessgreater(x, y) __builtin_islessgreater(x, y)
#define isunordered(x, y) __builtin_isunordered(x, y)
#else /* __GNUC__ < 3 */
/* helper */
extern int __cdecl __fp_unordered_compare (long double, long double);
#ifndef __NO_INLINE__
__CRT_INLINE int __cdecl
__fp_unordered_compare (long double x, long double y){
unsigned short retval;
__asm__ ("fucom %%st(1);"
"fnstsw;": "=a" (retval) : "t" (x), "u" (y));
return retval;
}
#endif /* !__NO_INLINE__ */
#define isgreater(x, y) ((__fp_unordered_compare(x, y) & 0x4500) == 0)
#define isless(x, y) ((__fp_unordered_compare(y, x) & 0x4500) == 0)
#define isgreaterequal(x, y) ((__fp_unordered_compare(x, y) & FP_INFINITE) == 0)
#define islessequal(x, y) ((__fp_unordered_compare(y, x) & FP_INFINITE) == 0)
#define islessgreater(x, y) ((__fp_unordered_compare(x, y) & FP_SUBNORMAL) == 0)
#define isunordered(x, y) ((__fp_unordered_compare(x, y) & 0x4500) == 0x4500)
#endif /* __GNUC__ < 3 */
#endif /* __cplusplus || _ISOC99_SOURCE */
_END_C_DECLS
#endif /* ! RC_INVOKED */
#endif /* !_MATH_H: $RCSfile: math.h,v $: end of file */
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